Fixed-Point Math Functions

MATLAB^® functions that support fixed-point data types

Create and manipulate fixed-point matrices and arrays. Use arithmetic, linear algebra, trigonometric, statistics, and complex math functions that support fixed-point data types.

Functions

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Array and Matrix Operations

Array Creation

`colon, :`	Create vectors, array subscripting
`eye`	Create identity matrix with fixed-point properties
`ones`	Create array of all ones with fixed-point properties
`zeros`	Create array of all zeros with fixed-point properties

Array and Matrix Manipulation

`horzcat`	Concatenate multiple `fi` objects horizontally
`sort`	Sort elements of real-valued `fi` object in ascending or descending order
`subsasgn`	Subscripted assignment
`subsref`	Subscripted reference
`vertcat`	Concatenate `fi` object arrays vertically

Basic Array and Matrix Information

`isequivalent`	Determine if two `numerictype` objects have equivalent properties
`isfloat`	Determine whether input is floating-point data type
`max`	Largest element in array of `fi` objects
`min`	Smallest element in array of `fi` objects
`numel`	Number of data elements in `fi` array

Array and Matrix Operators

`ctranspose`	Complex conjugate transpose of `fi` object
`minus`	Matrix difference between `fi` objects
`mpower`	Fixed-point matrix power (^)
`mrdivide`	Right-matrix division
`mtimes`	Matrix product of `fi` objects
`plus`	Matrix sum of `fi` objects
`qr`	Orthogonal-triangular decomposition
`rdivide`	Right-array division
`shiftdata`	Shift data to operate on specified dimension
`sum`	Sum of `fi` array elements
`times`	Element-by-element multiplication of `fi` objects
`uminus`	Negate elements of `fi` object array
`unshiftdata`	Inverse of `shiftdata`

Linear System Solvers and Matrix Factorizations

`fixed.backwardSubstitute`	Solve upper-triangular system of equations through backward substitution (Since R2020b)
`fixed.forwardSubstitute`	Solve lower-triangular system of equations through forward substitution (Since R2020b)
`fixed.jacobiSVD`	Fixed-point Jacobi singular value decomposition (Since R2023a)
`fixed.qlessQR`	Q-less QR decomposition (Since R2020b)
`fixed.qlessQRUpdate`	Update QR factorization (Since R2020b)
`fixed.qrAB`	Compute C = Q'B and upper-triangular factor R (Since R2020b)
`fixed.qrMatrixSolve`	Solve system of linear equations Ax = B for x using QR decomposition (Since R2020b)
`fixed.qlessQRMatrixSolve`	Solve system of linear equations (A'A)X = B for X using Q-less QR decomposition (Since R2020b)
`fixed.svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (Since R2022b)
`svd`	Fixed-point Golub-Kahan-Reinsch singular value decomposition (Since R2022b)

Specialized Matrices

toeplitz Create Toeplitz matrix

Activations

cordicsigmoid CORDIC-based approximation of sigmoid activation (Since R2023b)

Complex Math

`abs`	Absolute value of `fi` object
`complex`	Construct complex `fi` object from real and imaginary parts
`conj`	Complex conjugate of `fi` object
`sign`	Perform sign function (signum function) on array

Constants

`eps`	Quantized relative accuracy for `fi` or `quantizer` objects
`intmax`	Largest positive stored integer value representable by `numerictype` of `fi` object
`intmin`	Smallest stored integer value representable by `numerictype` of `fi` object

Exponentials

`nextpow2`	Exponent of next higher power of 2 of `fi` object (Since R2020a)
`pow2`	Efficient fixed-point multiplication by 2^K
`power`	Fixed-point element-wise power
`sqrt`	Square root of `fi` object

Math Operations

`accumneg`	Subtract two `fi` objects or values
`accumpos`	Add two `fi` objects or values
`add`	Add two arrays using `fimath` object
`atan2`	Four-quadrant inverse tangent of fixed-point values
`ceilDiv`	Round the result of division toward positive infinity (Since R2021a)
`conv`	Convolution and polynomial multiplication of `fi` objects
`cos`	Cosine of `fi` object in radians
`divide`	Divide two `fi` objects
`fixDiv`	Round the result of division toward zero (Since R2021a)
`floorDiv`	Round the result of division toward negative infinity (Since R2021a)
`mpy`	Multiply two arrays using `fimath` object
`nearestDiv`	Round the result of division toward the nearest integer (Since R2021a)
`nnz`	Number of nonzero elements in `fi` object (Since R2020b)
`normalizedReciprocal`	Compute normalized reciprocal (Since R2020a)
`sin`	Sine of fixed-point values
`sqrt`	Square root of `fi` object
`sub`	Subtract two arrays using `fimath` object

Radix Conversion

`bin`	Unsigned binary representation of stored integer of `fi` object
`bin2num`	Convert two's complement binary string to number using `quantizer` object
`dec`	Unsigned decimal representation of stored integer of `fi` object
`dec2base`	Convert decimal integer to its base-n representation for `fi` objects (Since R2021b)
`dec2bin`	Convert decimal integer to its binary representation for `fi` objects (Since R2021b)
`dec2hex`	Convert decimal integer to its hexadecimal representation for `fi` objects (Since R2021b)
`hex`	Hexadecimal representation of stored integer of `fi` object
`hex2num`	Convert hexadecimal string to number using `quantizer` object
`num2bin`	Convert number to binary representation using `quantizer` object
`num2hex`	Convert number to hexadecimal equivalent using `quantizer` object
`num2int`	Convert number to signed integer using `quantizer` object
`oct`	Octal representation of stored integer of `fi` object
`sdec`	Signed decimal representation of stored integer of `fi` object

Relational Operators

`eq`	Determine whether real-world values are equal
`ge`	Determine whether real-world value of one array is greater than or equal to another
`gt`	Determine whether real-world value of one array is greater than another
`le`	Determine whether real-world value of one array is less than or equal to another
`lt`	Determine whether real-world value of one array is less than another
`ne`	Determine whether real-world values of two arrays are not equal

Rounding and Remainders

Rounding Functions

`ceil`	Rounds toward positive infinity
`convergent`	Round toward nearest integer with ties rounding to nearest even integer
`fix`	Round toward zero
`floor`	Round toward negative infinity
`nearest`	Round toward nearest integer with ties rounding toward positive infinity
`round`	Round `fi` object toward nearest integer or round input data using `quantizer` object

Modulus and Remainder Functions

`mod`	Modulus after division for `fi` objects
`modByConstant`	Modulus after division by a constant denominator (Since R2021a)

Statistics

`errmean`	Mean of quantization error
`errpdf`	Probability density function of quantization error
`errvar`	Variance of quantization error
`logreport`	Quantization report
`maxlog`	Log maximums
`minlog`	Log minimums
`noperations`	Number of quantization operations by `quantizer` object
`noverflows`	Number of overflows
`nunderflows`	Number of underflows
`resetlog`	Clear log for `fi` or `quantizer` object
`mean`	Average or mean value of fixed-point array
`median`	Median value of fixed-point array